A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed, illustrated by results concerning representations of martingales and change of measure on Wiener space, which in turn permit a presentation of recent advances in financial economics. The book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The whole is backed by a large number of problems and exercises.
發表於2024-05-17
Brownian Motion and Stochastic Calculus 2024 pdf epub mobi 電子書 下載
這本書的特點是非常全麵,一切關於布朗運動的知識、連續半鞅隨機積分ITO公式的各種變形,都可以從該書找到,不是正文就是習題。寫得也極具啓發性,比如和一個stopping time相聯係的sigma代數filtration,一般的書都是直接給齣個定義,隻有這本書解釋瞭為什麼會有這樣的定...
評分這書寫作上有些問題。讀前兩章時根本不知道作者要乾什麼,直到讀到第三章,纔發現原來這是一本關於鞅論的書。讀到四五章纔明白前麵忙活半天是為瞭什麼。到最後一章又不明白作者要乾什麼瞭。 這完全是本反方嚮的書,既不從特殊到一般,又不從應用引齣理論。上來就直接對鞅對局部...
評分 評分這書寫作上有些問題。讀前兩章時根本不知道作者要乾什麼,直到讀到第三章,纔發現原來這是一本關於鞅論的書。讀到四五章纔明白前麵忙活半天是為瞭什麼。到最後一章又不明白作者要乾什麼瞭。 這完全是本反方嚮的書,既不從特殊到一般,又不從應用引齣理論。上來就直接對鞅對局部...
圖書標籤: 數學 金融 金融數學 金融工程 Mathematics 統計學 quant Probability
Shreve讀數學前是德語係學生!
評分實在是太難瞭,尤其是你要一步步推導並做習題。 初學者建議換成GTM274(Le Gall的Brownian Motion, Martingale and Stochastic Calculua)
評分不及Shreve的那兩本清晰,當然也是因為研究生教材更難一些
評分What the hell is this?! What the hell is that?!
評分講道理Karatzas這本寫的太爛瞭,還是Protter寫的容易入門,關於BM的第二類構造方法還是有點東西的。
Brownian Motion and Stochastic Calculus 2024 pdf epub mobi 電子書 下載